This gets cited here weekly, usually second-hand, so it is worth setting out what it does and does not establish.
The distinction that matters is unopened versus in use. Unopened vials are stable refrigerated for their labelled shelf life and tolerate a limited excursion to room temperature. Once reconstituted, the clock is much shorter and is set by the preservative rather than by the peptide — bacteriostatic water's benzyl alcohol is what buys you multiple draws over weeks. Sterile water has no preservative and turns a multi-dose vial into a single-use one.
Where I think it is weakest: the follow-up is short relative to how long people actually take these drugs, so durability is an assumption here rather than a finding.
So the question, as narrowly as I can put it: what a temperature excursion actually does, and what distinguishes an unopened vial from one already in use. Tell me what I have not thought of.
Note on sourcing:
Figures above are from the primary publication rather than the press summary. If a number here disagrees with one you have, post yours and we will work out which of us is reading a secondary source.